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Abruptly autofocusing beams were proposed and tested for a variety of applications such as optical manipulation, yet their trapping performance associated with the optical forces and trap stiffness remains largely unexplored. In this work, we design and demonstrate specially modulated autofocusing beams. We theoretically and experimentally show improved properties of such beams and their trapping capabilities as compared to their unmodulated counterparts. In particular, an autofocusing beam tailored with a Bessel function exhibits a shorter focal length and a much stronger peak intensity than that of an unmodulated circular Airy beam. Moreover, we perform optical tweezer experiments using both the modulated and unmodulated autofocusing beams to trap microbeads and red blood cells for direct comparison, and find that the Bessel-modulated beam displays an enhanced trapping capability, thanks to a stronger optical trapping force due to its peculiar intensity landscape. Compared with the conventional circular Airy beams, optical tweezers based on our modulated autofocusing beams exhibit a superior performance, which may lead to new photonic tools for optical trapping and manipulation.

Abruptly autofocusing beams have attracted more and more attention because of their potential applications in optical manipulation. Here, we not only experimentally and theoretically investigate dynamical propagation properties of two-dimensional (2D) Airy--beam superpositions in free space and disordered media, but also study their stability, dynamical power flow, and trapping force properties from a different point. 2D Airy-beam superpositions have superior stability and can easily control their autofocusing propagations and trapping forces through a changing number of superimposing beams, truncated factor, scale factor, initial position, and the angle between two wings of 2D Airy beams. Based on the analysis of the evolution of power flow and trapping force, it is demonstrated that 2D Airy-beam superpositions repeat many autofocusing propagations, leading to a series of focuses and stable trapping positions to appear in propagation. Compared to traditional autofocusing beams, i.e., circular Airy beams and one-dimensional Airy-beam superpositions, 2D Airy-beam superpositions can show a better optical trapping performance in theory. Moreover, we used 2D Airy-beam superpositions as an optical tweezer to trap particles in the experiment and quantitatively analyzed trapping force properties such as trap stiffness via the power spectra method. The experimental results further demonstrate that 2D Airy-beam superposition can show better optical trapping ability than the circular Airy beam. Our work provides a systematic understanding of the propagation and trapping properties of 2D Airy-beam superpositions in theory and experiment. It is helpful for the further applications of autofocusing beams on the optical tweezer, especially in biomedical research.

We demonstrate a production of large-area $^{87}\mathrm{Rb}$ Bose-Einstein condensates (BECs) using a non-Gaussian optical dipole trap (ODT). The ODT is formed by focusing a symmetrically truncated Gaussian laser beam, and it is shown that the beam clipping causes the trap geometry to be elongated and flattened along the beam axis direction. In the clipped-Gaussian ODT, an elongated, highly oblate BEC of $^{87}\mathrm{Rb}$ is generated with a length and width of approximately 470 and $130\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m},$ respectively, where the condensate healing length is estimated to be $\ensuremath{\xi}\ensuremath{\approx}0.25\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$ at the trap center. The ODT is characterized to have a quartic trapping potential along the beam axis and the atom density of the condensate is uniform within 10% over $1000\ensuremath{\xi}$ in the central region. Finally, we discuss the prospect of conducting vortex shedding experiments using the elongated condensate.

We study the trapping of a ground-state cesium atom in a small region around the midpoint between two coupled identical parallel optical nanofibers. We suggest to use a blue-detuned guided light field in the odd $\mathcal{E}_z$-sine array mode to produce an optical potential with a local minimum of exact zero at the midpoint between the nanofibers. We find that the effects of the van der Waals potential on the total trapping potential around the minimum point are not significant when the fiber separation distance and the power of the guided light field are large. For appropriate realistic parameters, a net trapping potential with a significant depth of about 1 mK, a large coherence time of several seconds, and a large recoil-heating-limited trap lifetime of several hours can be obtained. We investigate the dependencies of the trapping potential on the power of the guided light field, the fiber radius, the wavelength of light, and the fiber separation distance., Comment: arXiv admin note: text overlap with arXiv:2012.06078

We study the optical forces experienced by a dielectric microsphere placed in a nonparaxial vector self-accelerating beam. Following the beam's peak intensity (or the main lobe), where the dominant transverse trapping appears, the longitudinal optical force is found to switch from a purely pushing case to an impure case involving pulling forces. The pulling forces tend to appear away from the optimal transverse trapping position, particularly for large particles but populate largely within the transverse trapping potential. In terms of magnitude, such forces can be comparable to the transverse ones when manipulating small particles. The cases of both Mie and Rayleigh particles are discussed. Our work opens the possibility to uncover the pulling effect in nonparaxial accelerating beams, which may lead to applications in optical trapping and manipulation.

We investigate multicomponent fermions in a flat band and predict experimental signatures of non-Fermi liquid behavior. We use dynamical mean-field theory to obtain the density, double occupancy and entropy in a Lieb lattice for $\mathcal{N} = 2$ and $\mathcal{N} = 4$ components. We derive a mean-field scaling relation between the results for different values of $\mathcal{N}$, and study its breakdown due to beyond-mean field effects. The predicted signatures occur at temperatures above the N\'eel temperature and persist in presence of a harmonic trapping potential, thus they are observable with current ultracold gas experiments., Comment: 6 pages, 5 figures and and a supplementary material

For conventional ion traps, the trapping potential is close to independent of the electronic state, providing confinement for ions dependent primarily on their charge-to-mass ratio $Q/m$. In contrast, storing ions within an optical dipole trap results in state-dependent confinement. Here we experimentally study optical dipole potentials for $^{138}\mathrm{Ba}^+$ ions stored within two distinctive traps operating at 532 nm and 1064 nm. We prepare the ions in either the $6\mathrm{S}_{\mathrm{1/2}}$ electronic ground or the $5\mathrm{D}_{\mathrm{3/2}}$/ $5\mathrm{D}_{\mathrm{5/2}}$ metastable excited state and probe the relative strength and polarity of the potential. On the one hand, we apply our findings to selectively remove ions from a Coulomb crystal, despite all ions sharing the same $Q/m$. On the other hand, we deterministically purify the trapping volume from parasitic ions in higher-energy orbits, resulting in reliable isolation of Coulomb crystals down to a single ion within a radio-frequency trap., Comment: 9 pages, 5 figures

We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spinorbit states. By analyzing the single particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement., Comment: 9 pages, 6 figures

In most experiments with atoms trapped in optical lattices, the transverse size of the optical lattice beams is of the order of tens of micrometers, and loading many atoms into smaller optical lattices has not been carefully investigated. We report trapping 1500 $^{171}\mathrm{Yb}$ atoms in a one-dimensional optical lattice generated by a narrow cavity mode at a distance of 0.14 mm from a mirror surface. The simplest approach of loading atoms from a mirror magneto-optical trap overlapped with the cavity mode allows the adjustment of the loading position by tuning a uniform bias magnetic field. The number of atoms trapped in the optical lattice exhibits two local maxima for different lattice depths, with a global maximum in the deeper lattice. These results open a way to quantum mechanical manipulation of atoms based on strong interaction with a tightly focused light field.

We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the limiting case of chiral (or one-way) coupling. We investigate various quantum optical properties of the system, including its steady-state populations, power spectrum, and second-order correlation functions, and outline the characteristic features which emerge in each quantity as one sweeps through the nontrivial landscape of effective complex couplings. Most importantly, we reveal instances of population trapping, unexpected spectral features, and strong emission correlations., This work was funded by the Spanish MINECO, via the Juan de la Cierva program (C.A.D.), CLAQUE Project No. FIS2015-64951-R (A.I.F.-D. and E.d.V.), and the “María de Maeztu” Programme for Units of Excellence in R & D (Grant No. CEX2018-000805-M) (A.I.F.-D. and E.d.-V). This work was also supported by a Leonardo Grant for researchers and cultural creators, from the BBVA Foundation (A.I.F.-D.).

We theoretically investigate the use of fast pulsed two-qubit gates for trapped ion quantum computing in a two-dimensional microtrap architecture. In one dimension, such fast gates are optimal when employed between nearest neighbours, and we examine the generalisation to a two-dimensional geometry. We demonstrate that fast pulsed gates are capable of implementing high-fidelity entangling operations between ions in neighbouring traps faster than the trapping period, with experimentally demonstrated laser repetition rates. Notably, we find that without increasing the gate duration, high-fidelity gates are achievable even in large arrays with hundreds of ions. To demonstrate the usefulness of this proposal, we investigate the application of these gates to the digital simulation of a 40-mode Fermi-Hubbard model. This also demonstrates why shorter chains of gates required to connect arbitrary pairs of ions makes this geometry well suited for large-scale computation.

The present paper determines the precise values of magic wavelengths corresponding to the clock transitions ${5}^{2}S\text{--}{4}^{2}D$ of the ${\mathrm{Y}}^{2+}$ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.

We investigate theoretically the application of Sawtooth Wave Adiabatic Passage (SWAP) in a 1D magneto-optical trap (MOT). As opposed to related methods that have been previously discussed, our approach utilizes repeated cycles of stimulated absorption and emission processes to achieve both trapping and cooling, thereby reducing the adverse effects that arise from photon scattering. Specifically, we demonstrate this method's ability to cool, slow, and trap particles with fewer spontaneously emitted photons, higher forces and in less time when compared to a traditional MOT scheme that utilizes the same narrow linewidth transition. We calculate the phase space compression that is achievable and characterize the resulting system equilibrium cloud size and temperature., 14 pages, 7 figures. Major changes: reordering of detuning definitions, omission of what was originally Fig. 4, clarifications in Figs. 2-4 and 6-7, addition of reference 9, and restructuring of Sections 3 and 4 for clarity

Radio-frequency-induced micromotion in trapped ion systems is typically minimized or circumvented to avoid off-resonant couplings for adiabatic processes such as multi-ion gate operations. Nonadiabatic entangling gates (so-called ``fast gates'') do not require resolution of specific motional sidebands and are, therefore, not limited to time scales longer than the trapping period. We find that fast gates designed for micromotion-free environments have a significantly reduced fidelity in the presence of micromotion. We show that when fast gates are designed to account for the radio-frequency-induced micromotion, they can, in fact, outperform fast gates in the absence of micromotion. The state-dependent force due to the laser induces energy shifts that are amplified by the state-independent forces producing the micromotion. This enhancement is present for all trapping parameters and is robust to realistic sources of experimental error. This result paves the way for fast two-qubit entangling gates on scalable two-dimensional architectures, where micromotion is necessarily present on at least one interion axis.

The dynamics of molecules in strong laser fields is much more complicated than that of atoms. For example, molecules can break up through dissociative single ionization, in which the electronic dynamics and nuclear dynamics are strongly correlated with each other. In this work we develop a quantitative theory based on the strong-field approximation to describe the dissociative single ionization of a hydrogen molecule, which allows us to schematically investigate the electron-nuclear energy sharing in the dissociative and the nondissociative single ionization of ${\text{H}}_{2}$ induced by intense laser pulses. Under different parameters of the laser pulse, we are able to discuss various types of dynamics in the framework of energy sharing, such as bond softening, dynamical quenching, vibrational trapping, and inverse bond hardening. In particular, we find drastic differences in the electron-nuclear energy sharing for UV and IR pulses. The current theoretical framework can potentially be extended to examine other strong-field phenomena in which the dynamics of different particles are correlated.

Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly in the case of a relatively large winding number. Here we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two co-axial counter-propagating optical vortex beams. We focus on the atomic transition $6^2S_{1/2}\rightarrow 5^2D_{5/2}$ in Cs which is a dipole-forbidden, but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near-resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We show how the optical forces generate the motion of the atoms trapped within the quadrupole potential, illustrating the results using typical experimentally accessible parameters., Comment: 7 pages; 9 figures

A configuration to identify the stochastic effect of the quantum radiation reaction is proposed, where electrons are put in a standing wave of two colliding ultraintense lasers. By comparing the simulation results of the semiclassical and quantum models, we find that if the semiclassical model is used, a particular trapping of electrons between two electric-field nodes is induced, which, however, does not exist once the correct quantum model is applied. This results in different features of the electron density, energy, and angular distributions, which can be measured in experiments.

We study the nonlinearities due to direct perturbation to the dark state in coherent population trapping (CPT). To extract the susceptibilities of the CPT atoms with respect to probe fields, we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone. With such a redefinition, we reveal that a CPT-based system displays an ultralarge, resonantly enhanced second-order cross susceptibility ${\ensuremath{\chi}}^{(2)}$ together with vanishing linear absorption. Physically, this effect is based on the CPT dark-state shift, which is traced to the six-photon parametric processes for all involved fields (including the dressing and probe fields). Because of the lack of the direct perturbation, this effect is absent in the electromagnetically induced transparency (EIT)-based system, in which only resonantly enhanced third-order (Kerr) susceptibility ${\ensuremath{\chi}}^{(3)}$ is obtainable but much weaker than the second-order one. The second-order nonlinearity, because of its stronger effect, can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.

We study strongly interacting ultracold spin-$1/2$ fermions in a honeycomb lattice in the presence of a harmonic trap. Tuning the strength of the harmonic trap we show that it is possible to confine the fermions in artificial structures reminiscent of graphene nanoflakes in solid state. The confinement on small structures induces magnetic effects which are absent in a large graphene sheet. Increasing the strength of the harmonic potential we are able to induce different magnetic states, such as a N\'eel-like antiferromagnetic or ferromagnetic state, as well as mixtures of these basic states. The realization of different magnetic patterns is associated with the terminations of the artificial structures, in turn controlled by the confining potential.

We report on the stable effective trapping of cold rubidium atoms by a method for a single optical trap in the near-optical resonant regime. An optical trap with the near-optical resonance condition consists of not only the dipole but also the radiative forces, while a trap using a far-off resonance dominates only the dipole force. We measure the spatial behaviors of the center-of-mass positions and the loading efficiencies of the trapped atoms in the near-optical resonant trap, by changing the detuning over the range of $\ensuremath{-}0.373$ to $\ensuremath{-}2.23$ THz from the ${\mathrm{D}}_{2}$ resonance. The time dependence of the spatial behavior in the trap indicates that the suitable positions for stably holding atoms are altered because the equilibrium condition between the optical dipole and the radiative forces depends on the trap laser detuning. The stable position, which is not a primary position of focus in the Gaussian beam optics, depends only on the laser detuning due to the change in the radiative force, while it is independent of the change in the laser intensity, which results in a balance between the radiative and dipole forces.

We have considered the Raman scattering in molecular media. Applying two laser fields in a two-photon resonance with vibrational transition, we have studied the role of rotational levels for excitation of vibrational coherence. It is shown that the molecular vibrational coherence strongly depends on the effect of coherent population trapping for rotational levels. The obtained results are important for applications of Raman spectroscopy to molecular detection in engineering, chemical, and biological applications.

We investigate quantum sensing of rotation with a multiatom Sagnac interferometer and present multipartite entangled states to enhance the sensitivity of rotation frequency. For studying the sensitivity, we first present a Hermitian generator with respect to the rotation frequency. The generator, which contains the Sagnac phase, is a linear superposition of a $z$ component of the collective spin and a quadrature operator of collective bosons depicting the trapping modes, which enables us to conveniently study the quantum Fisher information (QFI) for any initial states. With the generator, we derive the general QFI which can be of square dependence on the particle number, leading to the Heisenberg limit. We further find that the QFI may be of biquadratic dependence on the radius of the ring which confines the atoms, indicating that larger QFI is achieved by enlarging the radius. In order to obtain the square and biquadratic dependence, we propose to use partially and globally entangled states as inputs to enhance the sensitivity of rotation.

Hybrid quantum systems have the potential of mitigating current challenges in developing a scalable quantum computer. Of particular interest is the hybridization between atomic and superconducting qubits. We demonstrate a novel experimental setup for transferring and trapping ultracold atoms inside a millikelvin cryogenic environment, where interactions between atomic and superconducting qubits can be established, paving the way for hybrid quantum systems. $^{87}\text{Rb}$ atoms are prepared in a conventional magneto-optical trap and transported via a magnetic conveyor belt into a UHV compatible dilution refrigerator with optical access. We store $5\times10^{8}$ atoms with a lifetime of 794 seconds in the vicinity of the millikelvin stage., Comment: 7 pages, 10 figures

When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency which is close to the trap frequency, its many-body state becomes highly correlated, with the most well-known being the bosonic Laughlin state. To take into account that in a real experiment no trapping potential is ever exactly harmonic, we introduce an additional weak, quartic potential and demonstrate that the Laughlin state is highly sensitive to this extra potential. Our results imply that achieving these states experimentally is essentially impossible, at least for a macroscopic atom number.

We compute the spontaneous relaxation rate of a two-level atom in a planar cavity with parity ($\mathcal{P}$) and parity-time ($\mathcal{PT}$) symmetry. We find that at the center of a $\mathcal{PT}$-symmetric cavity the evanescent contribution to the relaxation rate is greatly suppressed. As this is the dominant relaxation pathway for cavities smaller than the transition wavelength, $\mathcal{PT}$-symmetric microcavities are able to suppress the spontaneous relaxation rate dramatically and, in some cases, reduce it to below the free-space level. The ability to reduce the relaxation rate and lengthen the excited-state lifetime has many applications in quantum control and can, for example, be used to increase atomic trapping times, improve photonic storage, and help maintain the coherence of atomic qubits.

We have designed and realized magnetic trapping geometries for ultracold atoms based on permanent magnetic films. Magnetic chip based experiments give a high level of control over trap barriers and geometric boundaries in a compact experimental setup. These structures can be used to study quantum spin physics in a wide range of energies and length scales. By introducing defects into a triangular lattice, kagome and hexagonal lattice structures can be created. Rectangular lattices and (quasi-)one-dimensional structures such as ladders and diamond chain trapping potentials have also been created. Quantum spin models can be studied in all these geometries with Rydberg atoms, which allow for controlled interactions over several micrometers. We also present some nonperiodic geometries where the length scales of the traps are varied over a wide range. These tapered structures offer another way to transport large numbers of atoms adiabatically into subwavelength traps and back., Comment: 9 pages, 10 figures

A theory of coherent transients is developed in which a sequence of optical pulses is incident on a sample of trapped atoms and gives rise to phase-matched emission from the sample. The trapping potential for the atoms can be state dependent, necessitating a quantum treatment of the center-of-mass motion. A source-field approach is followed, modified to account for the quantized motion of the atoms. The theory is illustrated with two examples, one involving the creation of ground-Rydberg level coherence in an optical lattice and the second Raman coherence between two ground-state sublevels of atoms in a dipole trap. For state-independent potentials, a comparison is made with a theory in which the center-of-mass motion is treated classically.

We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\mathrm{SWAP}}$ gates in ultracold atoms. We show that a significant speedup can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes the accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but for comparison with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.

We report the measurement of the photoionization cross sections of the $5{S}_{1/2}$ and $5{P}_{3/2}$ states of $^{87}\mathrm{Rb}$ in a two-species Hg and Rb magneto-optical trap (MOT) by the cooling laser for Hg. The photoionization cross sections of Rb in the $5{S}_{1/2}$ and $5{P}_{3/2}$ states at 253.7 nm are determined to be ${1}_{\ensuremath{-}1}^{+4.3}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\phantom{\rule{0.28em}{0ex}}{\text{cm}}^{2}$ and $4.63(30)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\phantom{\rule{0.28em}{0ex}}{\text{cm}}^{2}$, respectively. To measure the $5{S}_{1/2}$ and $5{P}_{3/2}$ state fractions in the MOT we detected the photoionization rate of the $5{P}_{3/2}$ state by an additional 401.5 nm laser. The photoionization cross section of Rb in the $5{P}_{3/2}$ state at 401.5 nm is determined to be $\text{1.18(10)}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}\phantom{\rule{0.28em}{0ex}}{\text{cm}}^{2}$.

The off-resonant AC Stark shift for coherent population trapping (CPT) resonances probed with Ramsey spectroscopy is investigated experimentally and theoretically. Measurements with laser-cooled $^{87}$Rb atoms show excellent quantitative agreement with a simple theory. The shift depends on the relative intensity of the two CPT light fields, but depends only weakly on the total intensity. Since the origin of the shift is through couplings of the interrogation light to off-resonant excited state hyperfine levels, the size and sign of the shift depend on the specific interrogation scheme. However, the simple theory shows that for several commonly used interrogation schemes the off-resonant shift goes to zero at specific values of this relative intensity., 7 pages, 7 figures

We study the confinement-induced resonance (CIR) of $^{173}$Yb atoms near an orbital Feshbach resonance in a quasi-one-dimensional tube with transversal anisotropy. By solving the two-body scattering problem, we obtain the location of CIR for various anisotropy ratio and magnetic field. Our results show that the anisotropy of the trapping potential can serve as an additional knob to tune the location of CIR. In particular, one can shift the location of CIR to the region attainable in current experiment. We also study the energy spectrum of the system and analyze the properties of CIR from the perspective of bound states. We find that as the orbital Feshbach resonance acquires two nearly degenerate scattering channels, which in general have different threshold energies, CIR takes place when the closed channel bound state energy becomes degenerate with one of the thresholds., Comment: 8 pages, 5 figures

We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond mean-field, Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local density approximation, with two different schemes, to model different trapping potentials in the tightly-confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly-confined transverse direction, and describe its behavior as functions of the dimensionality, from two- to three-dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of $^{6}$Li and $^{40}$K atoms.

We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance and interplay of the molecular rotational structure, anisotropic interactions, spin-rotation coupling, electric and magnetic fields, and harmonic trapping potential are examined in detail, and compared to the system of two harmonically trapped distinguishable atoms. Presented model and results may provide microscopic parameters for molecular many-body Hamiltonians, and may be useful for the development of bottom-up molecule-by-molecule assembled molecular quantum simulators., Comment: 16 pages, 11 figures

We present a numerical study of the dynamic response of a confined superfluid Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the full Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigar-shaped $^6$Li gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potential but that it is determined by the details of the quench. Thus, we report the emergence of a pure Goldstone mode of the BCS gap that --in contrast to situations in many previous studies-- maintains its gapless excitation spectrum predicted by the Goldstone theorem. Furthermore, we observe that the size-dependent superfluid resonances resulting from the atypical BCS-BEC crossover have a direct impact on this Goldstone mode. Finally, we find that the interaction quench-induced Goldstone mode leads to a low-frequency in-phase oscillation of the single-particle occupations with complete inversion of the lowest-lying single-particle states which could provide a convenient experimental access to the pure gapless Goldstone mode., Comment: This article supersedes our previous publication arXiv:1511.04239 [cond-mat.quant-gas]

We apply a recently developed effective string theory for vortex lines to the case of two-dimensional trapped superfluids. We do not assume a perturbative microscopic description for the superfluid, but only a gradient expansion for the long-distance hydrodynamical description and for the trapping potential. For any regular trapping potential, we compute the spatial dependence of the superfluid density and the orbital frequency and trajectory of an off-center vortex. Our results are fully relativistic, and in the non-relativistic limit reduce to known results based on the Gross-Pitaevskii model. In our formalism, the leading effect in the non-relativistic limit arises from two simple Feynman diagrams in which the vortex interacts with the trapping potential through the exchange of hydrodynamical modes., Comment: 8 pages, 4 figures

We experimentally investigate $\sigma^+$-$\sigma^-$ polarization gradient cooling~(PGC) of a single $^{87}$Rb atom in a tightly focused dipole trap and show that the cooling limit strongly depends on the polarization of the trapping field. For optimized cooling light power, the temperature of the atom reaches~$10.4(6)\,\mu$K in a linearly polarized trap, approximately five times lower than in a circularly polarized trap. The inhibition of PGC is qualitatively explained by the fictitious magnetic fields induced by the trapping field. We further demonstrate that switching the trap polarization from linear to circular after PGC induces only minor heating., Comment: 6 figures, 5 pages

We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonator coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamic equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We predict that a transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping in the asymmetric BJJs. Our results opens up a way to demonstrate BJJ with two-phonon exchange interaction and can be applied to other systems, such as the optical and microwave systems., Comment: 7 pages, 7 figures

Observations of center of mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time scale mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature., Comment: 10 pages, 11 figures, published version

Quantum gases of rare-earth elements are of interest due to the large magnetic moment of many of those elements, leading to strong dipole-dipole interactions, as well as an often nonvanishing orbital angular momentum in the electronic ground state, with prospects for long coherence time Raman manipulation, and state-dependent lattice potentials. We report on the realization of a Bose-Einstein condensate of erbium atoms in a quasielectrostatic optical dipole trap generated by a tightly focused midinfrared optical beam derived from a $\textrm{CO}_2$ laser near 10.6$\mu$m in wavelength. The quasistatic dipole trap is loaded from a magneto-optic trap operating on a narrow-line erbium laser cooling transition near 583nm in wavelength. Evaporative cooling within the dipole trap takes place in the presence of a magnetic field gradient to enhance the evaporative speed, and we produce spin-polarized erbium Bose-Einstein condensates with $3\times10^4$ atoms., Comment: 5 pages, 5 figures

A method for efficiently trapping nanoparticles using a dielectrophoresis (DEP)-assisted plasmonic trap is presented. The proposed method overcomes the range limitations of a conventional plasmonic trap by employing a long-range DEP force to draw a nanoparticle closer to the plasmonic trap. To create the plasmonic trap, a $\mathsf{C}$-shaped engraving is used as it can trap a nanoparticle in a very small volume near the surface. A nanopillar is selected as the electrode to generated the DEP force as its height allows the force to extend further away from the surface. Extensive numerical simulations are performed to evaluate the performance improvement of the proposed scheme over conventional plasmonic trapping methods. The simulations show that the proposed scheme increases the probability of a successful trapping event by a factor of approximately three.

Optical microtraps provide a strong spatial confinement for laser-cooled atoms. They can, e.g., be realized with strongly focused trapping light beams or the optical near fields of nano-scale waveguides and photonic nanostructures. Atoms in such traps often experience strongly spatially varying AC Stark shifts which are proportional to the magnetic quantum number of the respective energy level. These inhomogeneous fictitious magnetic fields can cause a displacement of the trapping potential that depends on the Zeeman state. Hitherto, this effect was mainly perceived as detrimental. However, it also provides a means to probe and to manipulate the motional state of the atoms in the trap by driving transitions between Zeeman states. Furthermore, by applying additional real or fictitious magnetic fields, the state-dependence of the trapping potential can be controlled. Here, using laser-cooled atoms that are confined in a nanofiber-based optical dipole trap, we employ this control in order to tune the microwave coupling of motional quantum states. We record corresponding microwave spectra which allow us to infer the trap parameters as well as the temperature of the atoms. Finally, we reduce the mean number of motional quanta in one spatial dimension to $\langle n\rangle=0.3 \pm 0.1$ by microwave sideband cooling. Our work shows that the inherent fictitious magnetic fields in optical microtraps expand the experimental toolbox for interrogating and manipulating cold atoms., Comment: 6 pages, 3 figures, comments welcome

The influence of the center of mass motion of a trapped two level system on efficient resonant single photon absorption is investigated. It is shown that this absorption process depends strongly on the ratio between the characteristic time scales of spontaneous photon emission and of the two level system's center of mass motion. In particular, if the spontaneous photon emission process occurs almost instantaneously on the time scale of the center of mass motion coherent control of the center of mass motion offers interesting perspectives for optimizing single photon absorption. It is demonstrated that this way time dependent modulation of a harmonic trapping frequency allows to squeeze the two level system's center of mass motion so strongly that high efficient single photon absorption is possible even in cases of weak confinement by a trapping potential., 9 pages, 5 figures

We report the development of quantum microscopic theory of quasi-resonant dipole-dipole interaction in the ensembles of impurity atoms imbedded into transparent dielectric and located into Fabry-Perot cavity. On the basis of the general approach we study the simultaneous influence of the cavity and resonant dipole-dipole interaction on the shape of the line of atomic transition as well as on light trapping in dense impurity ensembles. We analyze this influence depending on the size of the ensemble, its density, as well as on r.m.s. deviation of the transition frequency shifts caused by the symmetry disturbance of the internal fields of the dielectric medium. Obtained results are compared with the case when the cavity is absent. We show that the cavity can essentially modify cooperative polyatomic effects., 11 pages, 4 figures